Magda Komorníková

Magda Komorníková
Slovak University of Technology in Bratislava · Department of Mathematics

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75
Publications
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1,719
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August 1990 - present
Slovak University of Technology in Bratislava
Position
  • Professor

Publications

Publications (75)
Chapter
Full-text available
In this paper we focus our attention on multi-dimensional copula models of returns of the indexes of selected prominent international financial markets. Our modeling results, based on elliptic copulas, 7-dimensional vine copulas and hierarchical Archimedean copulas demonstrate a dominant role of the SPX index among the considered major stock indexe...
Chapter
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We analyzed quarterly seasonally-filtered time series (OECD link) of GDP in EURO per capita for the V4 countries (Visegrad treaty - Czech republic, Hungary, Poland, Slovakia) and Germany in the period 1996/Q1 – 2018/Q1. First, ARIMA models were used to clear the temporal dependence, then marginal distribution functions were utilized to standardize...
Chapter
Full-text available
This chapter analyzes seasonally adjusted quarterly data for the V4 countries, Czech Republic (Cz), Hungary (Hu), Poland (Pl) and Slovakia (Sk), for the period 1995/Q1‐2016/Q3. It investigates parallel changes in GDP of these countries using four‐dimensional Vine copula models. The chapter applies ARIMA‐GARCH filters to logarithms of the data of th...
Conference Paper
We propose a new method for constructing fuzzy measures. This method is based on a fixed aggregation function A, similarity measure S and a vector \(\mathbf {x} \in [0,1]^n\). Some illustrative examples yielding parametric families of fuzzy measures are given, and some properties of our method are studied.
Conference Paper
In this paper we provide an extension of special parametric class of perturbations of an arbitrary copula (given in [3]) that represent a partial generalization of the FGM family of copulas for parameters from the unit interval. However the FGM family is defined for parameters from the interval \([-1,1]\). We present a construction of perturbations...
Article
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This article deals with a method of how to acquire approximate displacement vibration functions. Input values are discrete, experimentally obtained mode shapes. A new improved approximation method based on the modal vibrations of the deck is derived using the least-squares method. An alternative approach to be employed in this paper is to approxima...
Article
In this paper (which is a substantially extended version of a conference paper from AGOP 2015), we investigate the effects of specific class of perturbations of bivariate copulas on several measures of dependence (Spearman's rho, Blomqvist's beta, Gini's gamma, Kendall's tau), and tail dependence along both diagonal sections. It is demonstrated tha...
Article
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It is widely acknowledged that in the hydrological and meteorological communities, there is a continuing need to improve the quality of quantitative rainfall and river flow forecasts. A hybrid (combined deterministic-stochastic) modelling approach is proposed here that combines the advantages offered by modelling the system dynamics with a determin...
Article
This paper investigates the role of gold as a safe haven in international stock markets using various copula techniques to capture complex dependencies between stock markets and gold prices. It creates a new class of mix copulas from Clayton, Frank, Gumbel and Joe copulas. The paper employs parametric and nonparametric copulas to over 11 years of d...
Conference Paper
Full-text available
Stock and bond markets co–movements have been studied by many researchers. The object of our investigation is the development of three U.S. investment grade corporate bond indices. We concluded that the optimal 3D as well as partial pairwise 2D models are in the Student class with 2 degrees of freedom (and thus very heavy tails) and exhibit very hi...
Chapter
In this paper, we extend and modify our modelling [presented in the conference paper (Komorník and Komorníková, Predictive and descriptive models of mutual development of economic growth of Germany and selected non-traditional EU countries. In: ITISE 2015, International Work-Conference on Time Series, pp. 55–64. Copicentro Granada S.L, 2015)] of th...
Article
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In this paper, we extend our investigations of a special class of perturbations of copulas introduced in [7]. Despite a surprising fact that this kind of perturbations does not change the value of tail dependence of the original copulas, their use yielded models with considerably improved fitting qualities.
Chapter
Full-text available
In this paper, we extend our investigations of a special class of perturbations of copulas introduced in [6] as a partial generalization of Farlie – Gumbel – Morgenstern (FGM) class of copulas (for non–negative values of perturbation parameters). We construct an extension of such generalization for negative values of perturbation parameters and sho...
Article
Full-text available
In this paper (which is a substantially extended version of a con- ference paper from SMTDA 2016 [10]) we focus our attention to 3-dimensional copula models of returns of indices of US financial markets (various bond indices have been investigated in the literature much less than stock indices). We have gained interesting experience in constructing...
Conference Paper
Full-text available
In this paper, we synthesize and substantially extend our recent investigations of specific class of perturbations of bivariate cop-ulas and their effects on tail dependencies (along both diagonal sections). We show that those perturbations do not change the coefficients of tail dependencies along the main diagonal but linearly reduce their values...
Conference Paper
Full-text available
The aim of this paper is to investigate descriptive and predic-tive models for the growth of GDP (using seasonally adjusted quarterly data) for a group of selected EU countries containing Germany (as the leading EU economy), the 4 former East Block countries economically dominated by Germany (Czech Republic, Hungary, Poland, Slovakia) and Greece (a...
Article
After a brief presentation of the history of aggregation, we recall the concept of aggregation functions on [0; 1] and on a general interval /⊆ [—∞, ∞]. We give a list of basic examples as well as some peculiar examples of aggregation functions. After discussing the classification of aggregation functions on [0; 1] and presenting the prototypical e...
Conference Paper
The aim of this paper is to compare descriptive and predictive qualities of multivariate TAR models with threshold variables obtained via aggregation functions versus one-dimensional TAR models with endogenous as well as exogenous threshold variables. Time series of REIT indexes of 5 selected G7 countries (USA, Japan, Great Britain, France, Canada)...
Conference Paper
Full-text available
We have investigated the relations between 4 selected countries' (USA, Australia, Japan and UK) daily returns of the REIT (Real Estate Investment Trust) indexes in different time periods, determined by the recent global financial markets crises (July 1, 2008 – April 30, 2009). We have applied the fitting by copulas to the residuals of ARMA–GARCH fi...
Article
New types of constructions of bivariate copulas are introduced, discussed and exemplified. Based on a given copula C , we look for its perturbation into another copula CHCH, possibly close to C. A special stress is put on the perturbation of the basic copulas M, W, Π. Our results generalize several methods known from the literature, such as the Far...
Article
Full-text available
We propose a rather general construction method for bivariate copulas, generalizing some construction methods known from the literature. In some special cases, the constraints ensuring the output of the proposed method to be a copula are given. Our approach opens several new problems in copula theory.
Article
Full-text available
We have intensified studies of reflections of copulas, that we introduced recently, and found that their convex combinations exhibit potentially useful fitting properties for original copulas of the normal, Frank, Clayton and Gumbel types. We show that these properties enable us to construct interesting models for the relations between investment i...
Article
The traditional approach in the time series analysis of nitrate concentration in rivers is the decomposition of the original dataset followed by the linear modelling of residuals. The linear models are usually represented by the autoregressive models or their combination with moving average models. However, the advances in the nonlinear time series...
Article
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The autocorrelation function describing the linear dependence is not suitable for description of residual dependence of the regime-switching models. In this contribution, inspired by Zbl 1241.62126 P. Rakonczai, L. Márkus, A. Zempléni [”Autocopulas: investigating the interdependence structure of stationary time series”, Methodol. Comput. Appl. Prob...
Article
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This study examines two long-term time series of nitrate-nitrogen concentrations from the River Ouse and Stour situated in the Eastern England. The time series of monthly averages were decomposed into trend, seasonal and cyclical components and residuals to create a simple additive model. Residuals were then modelled by linear time series models re...
Article
Several classes of aggregation functions on bounded partially ordered sets are introduced and discussed. Considering their conjunctive and/or disjunctive attitude, some classification approaches are proposed, including several types of averaging aggregation functions. Aggregation functions on special cases of lattices and chains are discussed, too.
Conference Paper
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We apply the autocopula approach to residuals of Markov Switching models for various economic time series. Our results indicate substantial improvement of in-the-sample and out-of-the sample fitting.
Article
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Probability measures on intuitionistic fuzzy events were axiomatically characterized by B. Riečan in 2004 and subsequently studied in several papers. All these results can be straightforwardly transformed for the case of probability measures on interval–valued fuzzy sets. We give an alternative representation of all such probability measures. Compa...
Chapter
Full-text available
A general concept of aggregation on bounded posets is introduced and discussed. Up to general results, several particular results due to E.E. Kerre and his research group are recalled in the light of our approach. A special attention is paid to triangular norms on bounded posets.
Conference Paper
Full-text available
Classification of aggregation functions on bounded partially ordered sets is introduced and discussed, and its impact on classification of aggregation functions on bounded chains, especially on real intervals, is shown. As particular cases, disjunctive and conjunctive aggregation functions are given, as well as three types of averaging aggregation...
Article
Full-text available
The currencies of the Visegrád countries (Poland, the Czech Republic, Hungary,and Slovakia) have been considered by the international financial community as a basket ofcurrencies which are closely related, especially in times of their depreciations. On July 1,2008 the official terminal exchange rate SKK/EUR was fixed. During the following 8months,...
Conference Paper
In this paper the application of several nonlinear regime-switching time series models (SETAR, LSTAR and MSW) for annual river flows in the Tatra region is presented and their fitting and forecasting capabilities are compared.
Article
Flows of the Váh River and its tributaries are predominantly fed by snowmelt in the spring and convective precipitation in the summer. Therefore their regime properties exhibit seasonal patterns. Moreover the left and right side tributaries of the Váh River spring in different physiographic conditions in the High and Low Tatry Mountains. This provi...
Article
After the Second World War the nitrate concentrations in European water bodies changed significantly as the result of increased nitrogen fertilizer use and changes in land use. However, in the last decades, as a consequence of the implementation of nitrate-reducing measures in Europe, the nitrate concentrations in water bodies slowly decrease. This...
Article
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Štúdia sa zaoberá analýzou dlhých časových radov koncentrácie dusičnanov v rieke Ouse vo Východnom Anglicku. Časový rad priemerných mesačných koncentrácií dusičnanov bol rozložený na trendovú, sezónnu a cyklickú zložku a reziduá, ktoré boli k sebe pripočítané aby vytvorili jednoduchý aditívny model. Reziduá boli ďalej modelované zložitejšími lineár...
Article
Copulas stable under univariate conditioning are studied. Limit approach to construction of conditioning stable copulas is introduced and illustrated. In the class of Archimedean copulas, Clayton copulas are shown to be the only conditioning stable copulas. Conditioning stable singular copulas are also discussed and examples of non-Archimedean abso...
Article
Flows of the Váh River and its tributaries in the Tatry alpine mountain region in Slovakia are predominantly fed by snowmelt during the spring period and convective precipitation in the summer. Therefore their regime properties exhibit clear seasonal patterns. Moreover left and right side tributaries of the Váh River spring in different physiograph...
Article
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Copulas enabling to characterize the joint distributions of random vectors bymeans of the corresponding one-dimensional marginal distributions are presented anddiscussed. Some properties of copulas and several construction methods, especially when apartial knowledge is available, are included. Possible applications are indicated.
Article
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Several local and global properties of (extended) aggregation functions are discussed and their relationships are examined. Some special classes of averaging, conjunctive and disjunctive aggregation functions are reviewed. A special attention is paid to the weighted aggregation functions, including some construction methods
Article
Univariate conditioning of copulas is studied, yielding a construction method for copulas based on an a priori given copula. Based on the gluing method, the g-ordinal sum of copulas is introduced and a representation of copulas by means of g-ordinal sums is given. Though different right conditionings commute, this is not the case of right and left...
Article
Full-text available
The paper approaches problem of the flow forecasting for the Liptovská Mara reservoir with a hybrid modelling approach. The nonlinear hybrid modelling framework was investigated under the specific physiographic conditions of the High Core Mountains of Slovakia. The mean monthly flows of rivers used in this study are predominantly fed by snowmelt in...
Article
Full-text available
Aggregation operators are often needed when building preference relations in multicriteria decision making problems. Most existing approaches have limitations due to incomparability between decisions or ties due to the use of some aggregation operations that produce a ranking. The natural way of overcoming the lack of discrimination power is to ref...
Article
The paper approaches problem of the flow forecasting for the Liptovska Mara reservoir with a hybrid modelling approach. The nonlinear hybrid modelling framework was investigated under the specific physiographic conditions of the High Core Mountains of Slovakia. The mean monthly flows of rivers used in this study are predominantly fed by snowmelt in...
Article
A synthesis of recent development of regime-switching models based on aggregation operators is presented. It comprises procedures for model specification and identification, parameter estimation and model adequacy testing. Constructions of models for real life data from hydrology and finance are presented.
Article
Mean monthly flows of the Tatry alpine mountain region in Slovakia are predominantly fed by snowmelt in the spring and convective precipitation in the summer. Therefore their regime properties exhibit clear seasonal patterns. Positive deviations from these trends have substantially different features than the negative ones. This provides intuitive...
Conference Paper
A new method of construction of regime- switching models based on utilization of aggregation operators has been recently indicated in (2) (without any appropriate investigation of its practical usability). The goal of this paper is to provide a comprehensive exposition of the new method of model construction and mainly to explore their usability in...
Article
Full-text available
SUMMARY Advancements and automation on the field of measuring instruments provide us with quantum of more and more precise data to be further processed in an appropriate way. In our paper we deal with such a set of data arranged in time - time series - taken from continuous GPS observations on permanent station Borowiec which takes part in EUREF ne...
Article
A new class of Smooth Transition Autoregressive models, based on cubic spline type transition functions, has been introduced and subjected to comparison with models based on the traditional logistic transition functions. A very high degree of similarity between the two model classes has been demonstrated. The new class of models can be slightly pre...
Article
Aggregation (fusion) of several input values into a single output value is an indispensable tool not only of mathematics or physics, but of majority of engineering, economical, social and other sciences. The problems of aggregation are very broad and heterogeneous, in general. Therefore we restrict ourselves in this contribution to the specific top...
Article
Deterministic and stochastic approach to modeling common trends has been applied to time series of horizontal coordinates of the permanent GPS station Modra-Piesky (recorded weekly during the period of 4 years).
Article
Generated aggregation operators on continuous and discrete scales derived by means of a generating system are introduced. Linear generating systems are shown to be equivalent with the class of weighted means. The following classes are characterized: symmetric generated aggregation operators, idempotent generated aggregation operators, generated agg...
Article
Aggregation operators based on a fixed t-norm and on suitable transformations of processed data are introduced. A special attention is paid to the class of iterative compensatory operators containing also the classical arithmetic, geometric and harmonic means. Several properties of introduced operators are studied, e.g., the symmetry, the associati...
Conference Paper
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Article
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Discrete (ordinal) scales equipped with smooth triangular norms were introduced by Godo and Sierra. Smoothly generated aggregation operators on these scales are introduced, including the only smooth generated t-norm. The influence of additional properties on the introduced operators is discussed, leading to some surprising results. Some other resul...
Article
Several types of aggregation operators on fuzzy sets are discussed, all of them based on triangular norms and triangular conorms. The main stress is given to the operators allowing to compensate a low input value by another high input value, i. e., to the compensatory operators. We discuss only the pointwise aggregation and the crisp output can be...
Article
This article represents an attempt to follow some changes of mechanical properties of several different acid papers and an alkaline paper artificially aged in different quality archival boxes over 24 days at 103 degrees C and to evaluate these changes by comparing them with changes of the same papers aged outside the boxes under the same conditions...
Article
Full-text available
In recent years the ecological conditions in areas of important wetlands have markedly changed. One of the areas is also Kláštorské Lúky the national natural reservation wetland, which is situated in the Strážovské mountains in the northwest of the Slovak Republic. This study deals with the modeling and forecasting of discharge and rainfall time se...
Article
A new class of Smooth Transition Autoregressive models, based on cubic spline type transition functions, has been introduced and subjected to comparison with models based on the traditional logistic transition functions. A very high degree of similarity between the two model classes has been demonstrated. The new class of models can be slightly pre...
Article
We illustrate through several examples that business and economic time series tend to display such features as trends, seasonality, aberrant observations, conditionally varying variance, and/or nonlinearity. Before we can construct sensible out-of-sample forecasts of such time series, each of these features can best be described by a time series mo...
Article
Full-text available
Methods of time series analysis can be used to describe the generating mechanisms of the observed variables. A common method used in the time series analysis is modelling time series with linear models of the ARMA (autoregressive moving average model) class, where the modelled value of a time series depends entirely on the previous observations. Th...

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